Unit rationale, description and aim
This unit introduces pre-service teachers to the specialised mathematical knowledge essential for effective and confident teaching in early years and primary classrooms. Unlike general mathematical content knowledge, Mathematical Knowledge for Teaching (MKT) focuses on how mathematical ideas are structured, represented, and communicated (Ball, 2011).
The unit promotes mathematical proficiency through conceptual understanding, fluency, reasoning, and problem-solving across the core strands of the Australian Curriculum—number, algebra, geometry, measurement, statistics, and probability. Emphasis is placed on communicating mathematical thinking, using multiple representations, and developing positive dispositions toward mathematics.
Students critically explore foundational number concepts, including the historical and cross-cultural development of number systems, with attention to Indigenous perspectives. Topics also include early algebraic thinking, geometry, measurement, data, and chance.
Learning experiences combine collaborative and independent activities to build confidence in justifying solutions, selecting appropriate resources, and designing rich learning tasks. These skills support the development of deep mathematical understanding and responsive teaching practices.
This unit aims to build a strong foundation in MKT that informs future pedagogical decisions and prepares pre-service teachers for subsequent units focused on curriculum, pedagogy, and assessment.
Campus offering
No unit offerings are currently available for this unit.Learning outcomes
To successfully complete this unit you will be able to demonstrate you have achieved the learning outcomes (LO) detailed in the below table.
Each outcome is informed by a number of graduate capabilities (GC) to ensure your work in this, and every unit, is part of a larger goal of graduating from ACU with the attributes of insight, empathy, imagination and impact.
Explore the graduate capabilities.
Apply foundational concepts of mathematics (number...
Learning Outcome 01
Apply mathematical proficiencies (understanding, f...
Learning Outcome 02
Solve mathematical problems using correct terminol...
Learning Outcome 03
Defend problem solutions using appropriate represe...
Learning Outcome 04
Reflect on the importance of a positive mathematic...
Learning Outcome 05
Content
Topics will include:
- Mathematics and numeracy in the real world
- Exploring early number concepts, including number history and Indigenous understanding of number
- Place Value conventions – whole number
- Fraction concepts and constructs
- Place Value conventions – decimal fractions
- Understanding operations – arithmetic vs algebraic thinking
- Understanding operations – multiplication and division
- Geometry – 2D and geometric language
- Geometry – 3D and location
- Measurement concepts and the measuring process
- Foundations of data
- Understanding chance and probability
Assessment strategy and rationale
The assessment tasks and their weightings are designed to allow preservice teachers to progressively demonstrate achievement against the unit learning outcomes.
The assessments involve a variety of tasks to challenge students’ learning and enable differentiation of achievement and be equitable and ethical. The Hurdle incorporates a diagnostic test which enables students to develop a plan to build their mathematics knowledge to meet the knowledge and understanding expectations for primary teaching. Task 2 facilitates demonstration of problem-solving strategies, articulating mathematical thinking and reasoning through diagrams, mathematical notation and written explanations. Task 3 asks students to reflect critically on their learning journey throughout the unit, including evidence of this unit learning.
The assessment tasks for this unit are designed to demonstrate achievement of each learning outcome. To pass this unit, you are required to submit all assessment tasks and achieve a minimum overall passing grade of 50%.
As this unit contains practical, skill-based content, engagement with 80% of mathematics laboratory tutorials is recommended as per Section 5.9h of the ACU Assessment Procedure. For students in the online mode, there will be a nominated schedule of mathematics tutorial exercises equivalent to mathematics laboratory tutorials.
Overview of assessments
Hurdle Task: Online Numeracy Quiz Complete a for...
Hurdle Task: Online Numeracy Quiz
Complete a formative online numeracy quiz aligned to the testing framework for LaNTITE: Literacy.
Pass/Fail
Assessment Task 1: Problem-solving Logbook Comp...
Assessment Task 1: Problem-solving Logbook
Compile a logbook of six tasks drawn from tutorial experiences and covering the different strands of mathematics covered in the unit (number and algebra, measurement, geometry, probability and statistics). For each task, you will need to: (1) solve the problem, (2) justify the solution with mathematical reasoning, and (3) reflect on personal goal learning progression.
50%
Assessment Task 2: Learning in Mathematics Narrat...
Assessment Task 2: Learning in Mathematics Narrative
Reflect critically on your journey as a learner of mathematics, through a personal narrative, supported by a conceptual analysis of two core mathematical topics explored in the unit. Focus on developing mathematical self-awareness and explicitly communicating conceptual understanding that supports the development of deep Mathematical Knowledge for Teaching (MKT). Evidence of attending to the completion of tutorial activities should be used to support your personal narrative.
50%
Learning and teaching strategy and rationale
Learning and teaching strategies include a mix of student-centred problem-based learning, collaborative inquiry-based learning, and challenge-based learning. Learning and teaching will take place through a combination of self-directed studies, including online content, video clips, academic readings, weekly tasks, and reflection on learning experiences, and weekly contact hours for collaboration and discussion of problem-solving approaches and strategies.
Learning and teaching strategies are designed to be flexible and promote both collaborative learning and self-regulated and guided learning:
- Self-directed content online to enhance mathematical content knowledge
- Tutorial/workshop activities to engage in learning through active collaboration, designed to encourage and develop mathematical argumentation through peer learning to develop mathematical knowledge for teaching
- Reading/webinar/podcast schedule with recommendations that involve directed reading/viewing as well as self-directed study suggestions
Representative texts and references
Recommended Text and Documents
Zager, T. J. (2017). Becoming the math teacher you wish you’d had: Ideas and strategies from vibrant classrooms. Hawker Brownlow Education.
Oxford University Press UK (2013). Oxford Student’s Mathematics Dictionary. Oxford, UK: Oxford University Press
Recommended References
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.
Beswick, K., & Goos, M. (2018). Mathematics teacher educator knowledge: What do we know, and where to from here? Journal of Mathematics Teacher Education, 21, 417-427.
Clements, D. H., & Sarama, J. (2020). Learning and teaching early math: The learning trajectories approach (3rd ed.). Routledge.
Royer, J. M. (2003). Mathematical cognition. Information Age Publishing
Suggate, J., Davis, A. & Goulding, M. (2010). Mathematical knowledge for Primary teachers. Taylor and Francis Group.
Zager, T. J. (2017). Becoming the math teacher you wish you’d had: Ideas and strategies from vibrant classrooms. Routledge.